import numpy as np
import networkx as nx
from sklearn.preprocessing import normalize
from karateclub.estimator import Estimator
class NEU(Estimator):
r"""An implementation of `"NEU" <https://www.ijcai.org/Proceedings/2017/0544.pdf>`_
from the IJCAI 17 paper "Fast Network Embedding Enhancement via High Order Proximity Approximation".
The procedure uses an arbitrary embedding and augments it by higher order proximities wiht a recursive
meta learning algorithm.
Args:
L1 (float): Weight of lower order proximities. Defauls is 0.5
L2 (float): Weight of higer order proximities. Default is 0.25.
T (int): Number of iterations. Default is 1.
seed (int): Random seed value. Default is 42.
"""
def __init__(self, L1=0.5, L2=0.25, T=1, seed=42):
self.iterations = T
self.L1 = L1
self.L2 = L2
self.seed = seed
def _normalize_embedding(self, original_embedding):
r"""Normalizes matrix rows by their Frobenius norm.
Args:
original_embedding (Numpy array): An array containing an embedding
Return types:
normalized_embedding (Numpy array): An array containing a normalized embedding
"""
norms = np.linalg.norm(original_embedding, axis=1)
normalized_embedding = (original_embedding.T/norms).T
return normalized_embedding
def _update_embedding(self, graph, original_embedding):
r"""Performs the Network Embedding Update on the original embedding.
Args:
original_embedding (Numpy array): An array containing an embedding.
graph (NetworkX graph): The embedded graph.
Return types:
embedding (Numpy array): An array containing the updated embedding.
"""
embedding = self._normalize_embedding(original_embedding)
adjacency = nx.adjacency_matrix(graph, nodelist=range(graph.number_of_nodes()))
normalized_adjacency = normalize(adjacency, norm='l1', axis=1)
for _ in range(self.iterations):
embedding = (embedding +
self.L1*(normalized_adjacency @ embedding) +
self.L2*(normalized_adjacency @ (normalized_adjacency @ embedding)))
return embedding
def fit(self, graph, model):
r"""
Fitting a model and performing NEU.
Args:
* **graph** *(NetworkX graph)* - The graph to be embedded.
* **model** *(KC embedding model)* - Karate Club embedding.
"""
self._set_seed()
self._check_graph(graph)
self.model = model
self.model.fit(graph)
original_embedding = self.model.get_embedding()
self._embedding = self._update_embedding(graph, original_embedding)
def get_embedding(self):
r"""Getting the node embedding.
Return types:
* **embedding** *(Numpy array)* - The embedding of nodes.
"""
return self._embedding
